2) 4-cos²x=4sinx
4-(1-sin²x)=4sinx
sin²x-4sinx+3=0
y=sinx, -1≤y≤1
y²-4y+3=0
D=4²-4*3=16-12=4
√D=2
y₁=(4-2)/2=1
y₂=(4+2)/2=3- отбрасываем
sinx=1
x=π/2+2πn, где n целое
x=π/2
3) 5-2cosx=5√2sin(x/2)
5-2(cos²(x/2)-sin²(x/2))=5√2sin(x/2)
5-2(1-sin²(x/2)-sin²(x/2))=5√2sin(x/2)
5-2(1-2sin²(x/2))=5√2sin(x/2)
y=sin(x/2), -1≤y≤1
5-2(1-2y²)=5√2y
5-2+4y²=5√2y
4y²-5√2y+3=0
D=(5√2)²-4*4*3=25*2-48=2
√D=√2
y₁=(5√2-√2)/8=4√2/8=√2/2
y₂=(5√2+√2)/8=6√2/8=3√2/4>1 отбрасываем
sin(x/2)=√2/2
x/2=(-1)ⁿπ/4+πn, где n целое
x=(-1)ⁿπ/2+2πn
x=3π/2